A theorem about states on quantum logics. States on Jordan algebras
type: Item
instance of: scholarly article
title: A theorem about states on quantum logics. States on Jordan algebras
zbMATH Open document ID: 0543.46045
DOI: 10.1007/BF01018756
author: N. E. Zubov
published in: Theoretical and Mathematical Physics
publication date: 1983-01-01T00:00:00Z
review text: Let \({\mathcal A}\) be a Jordan algebra of operators on a complex Hilbert space and let \(\mu\) be a state on the projections of \({\mathcal A}\) (i.e. \(\mu\) is positive and orthoadditive). The author proves that every state \(\mu\) has an extension to a normal linear functional on \({\mathcal A}\), in case \({\mathcal A}\) is a continuous hyperfinite Jordan factor. He also notes that using a result of \textit{E. Christensen} [Commun. Math. Phys. 86, 529- 538 (1982; Zbl 0507.46052)], this can be extended to the case where \({\mathcal A}\) is an arbitrary continuous infinite Jordan algebra.
Mathematics Subject Classification ID: 46L99
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 17C65
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
zbMATH DE Number: 3863886
zbMATH Keywords: state on the projections
zbMATH Keywords: positive and orthoadditive
zbMATH Keywords: continuous hyperfinite Jordan factor
zbMATH Keywords: continuous infinite Jordan algebra
MaRDI profile type: Publication
cites work: Moufang plane and octonionic quantum mechanics
cites work: Jordan algebras of type I
cites work: Measures on projections and physical states
description: scientific article; zbMATH DE number 3863886